Procrustes problems (REF ) comprise of finding the optimal transformation between two matrices subject to certain constraints on the class of admissible transformations [1]}, [2]}, [3]}.
According to Greek mythology, Procrustes was a bandit who would
stretch or amputate the limbs of his victims to force
them to fit onto his bed.
Herein, \(X\)  plays the role of Procrustes' victim, \(Y\)  is the bed, and \(A\)  is the `treatment' (stretching or amputation).This terminology was first introduced by Hurley and Cattell [4]}.
Procrustes problems (REF ) seek to learn the treatment \(A\)  that best represents the data measurements \(X\)  and \(Y\) .
The minimization is usually phrased in the Frobenius norm.
Procrustes analysis finds relevance in a wealth of fields including sensory analysis [5]},
data visualization [6]},
neural networks [7]},
climate science [8]}, and
solid mechanics [3]}.
A summary is available in the monograph [2]}.
